Gate ECE 2017` closed

Question

Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further, Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

A) X is the mother-in-law of R.

B) P and R are not married to each other.

C) P is the son of X and Y.

D) Q can not be married to R.

Comments

@joshi

necessarily false means it always be false .. and in question nothing is given about only one child of ZW so we should not assume that  too..

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https://gateoverflow.in/313510/gate2017-ec-2-ga-7

https://aptitude.gateoverflow.in/3147/gate-general-aptitude-logical-reasoning-blood-relationship

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Option B should be correct answer

Answer 1

XY      ZW

|           |

Q P - - - R

    |       

   S
--- line means there is a possibility either true or false .
 | line means it directly inferred from question statements.
This is general scenario as we get from those given statements ..

P and R should be married to each other. otherwise Z can not be grandfather of S .

This is not always true .

Question said " Z and W are married and are parents of R. " there is a possibility that R may have another siblings ... there nothing is mention Z and W have only a single child so this possibility still exists !!

From question , it is clear that P is Not a child of Z and W .

P is child of X and Y only , but daughter of P is S and S's grandfather is Z so P is somehow related to Z .

That relation is only possible when Z and W have another child and P married to that child only ..so that means R can marry Q .

So in that case this statement " P and R are not married to each other " may not always false, it can be true also .

And " Q can not be married to R."  this statement  must necessarily be false .

As there is a possibility that Q can marry R . So Q can not marry R ever in any case is always false statement .

Hence correct statement is statement D .

Answer 2

ZW            XY

 |          /           \

R     P                Q

    |

   S

So, P and R must be married.

Option b is false.

Please correct me if I am wrong.

Comments

@Bikram Sir

http://www.gate.iitr.ernet.in/?page_id=485

ec set2, ques no. 62

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@Bikram sir,

if this is case than it is also wrong to assume that they have only one child because it is also not given that they have single child....

moreover according to qsn, i am taking both case(either P is child of Z and W or not a child of Z and W), because qsn is asking about necessarly fase, there is difference between necessarly false and false, necessarly false means false at every possibility..

now option B is not necessarly false because there exist a possibility which makes it true..

now option D is necessarly false beacuse it is given "Q can not be married to R" , because Q can be married to R 

if it was written "Q is not married to R" , than it might not be necessarly false...

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@joshi 

Very good analysis .. after answering this since yesterday i am thinking, i am missing something !!

Thank You for your inputs ...

if this is case than it is also wrong to assume that they have only one child because it is also not given that they have single child....

Yes, i completely agree with this , question said " Z and W are married and are parents of R. " there is a possibility that R may have another siblings ... there nothing is mention Z and W have only a single child so this possibility still exists !!

From question , it is clear that P is Not a child of Zand W .

P is child of Xand Y only , but daughter of P is S and S's grandfather is Z so P is somehow related to Z .

That relation is only possible when Zand W have another child and P married to that child only ..so that means R can marry Q .

So in that case this statement " P and R are not married to each other " may not always false, it can be true also .

And " Q can not be married to R."  this statement  must necessarly be false .

As there is a possibility that Q can marry R . So Q can not marry R ever in any case is always false .

if it was written "Q is not married to R" , than it might not be necessarly false..

yes i  completely agree .

hence correct option is statement D . 

Your last logic about can not and is not is very correct , because of this point D is correct option here .